Corrosion detection by differential thermography

ABSTRACT

A pulsed heat energized system for detecting corrosion or similar oxidation products located intermediate a layer of metal and an overlying layer of paint or other metal protective material. The system employs a continuing stream of radiant thermal energy pulses impinging on the external surface of the coated metal and responds to the phase angle difference between a waveform representing the energy pulses and a waveform representing the undulating temperature response of the paint surface to the energy pulses. Use of the system for detecting corrosion of a military or other aircraft in order to avoid stripping the aircraft for corrosion inspection and correction is contemplated. Enhanced independence of the corrosion detection from measurement variations and earlier detection of corrosion presence are achieved with respect to other corrosion arrangements.

RIGHTS OF THE GOVERNMENT

The invention described herein may be manufactured and used by or forthe Government of the United States for all governmental purposeswithout the payment of any royalty.;

BACKGROUND OF THE INVENTION

The U.S. Air Force spends millions of dollars each year inspectingaircraft for corrosion. Commercial aircraft owners and other governmentsalso spend similar or greater amounts for this purpose. A significantpart of this expense arises from the need to strip paint from thesurface of an aircraft to detect corrosion according to presentpractices. This stripping is necessary because it is difficult to detectcorrosion under paint by visual inspection until the paint blisters andsignificant damage to the painted aircraft has occurred. Whileinspection for corrosion remains as important as ever in order toprevent costly aircraft damage and even airframe failures, theenvironmental impact of the chemicals used for stripping purposes hasmade stripping practices even less desirable and prompted theinvestigation of means to detect corrosion without paint removal.

The patent art indicates aircraft manufacturers and others have alsobecome concerned by the need to inspect aircraft for corrosion and bythe related practice of stripping an aircraft in order to change itsappearance or visual signature. The U.S. Pat. No. 4,647,220 of M.J.Adams et al., for example, discloses a pulsed energy and electronicscanning inclusive method of detecting corrosion located below anaircraft coating in which the corrosion detection is based on detectionof surface temperature differentials resulting from exposing theaircraft to pulses of infrared energy. Notably, however the Adams et al.patent does not enjoy the advantages of detecting a phase angle lagbetween a pulsating energy waveform and the aircraft surface temperatureundulations produced by that waveform and is thereby more sensitive totesting variations than is the system of the present invention. Thesomewhat related practice of stripping an aircraft in order to changeits appearance or visual signature is disclosed, for example, in theU.S. Pat. Nos. 4,858,264 and 4,836,858 of T.J. Reinhart, which areassigned to the same assignee as the present patent. The patents andother documents referenced in each of the U.S. Patents identified heremay also be of background interest with respect to the presentinvention: each of these patents Is hereby incorporated by referenceherein.

SUMMARY OF THE INVENTION

The present invention provides a system for detecting phase lag betweenan applied periodic radiant heat input waveform and the temperature of apainted surface of, for example, an aircraft in order to providedetection of corrosion at an earlier stage and with less testingvariable sensitivity than previous corrosion detection methods. Thedisclosed system does not require removal of the paint nor applicationof a high emissivity coating or toxic chemicals and is non-contacting.

It is therefore an object of the present invention to provide for thenon destructive testing detection of subsurface corrosion or rusting oroxidized disintegration of a metallic surface.

It is another object of the present invention to provide detection ofmetallic corrosion that is hidden by paint or other organic coatings.

It is another object of the invention to provide detection of metalliccorrosion that is hidden by the paint or other organic coatings appliedto an aircraft.

It is another object of the invention to provide detection of hiddencorrosion of the aluminum or other lightweight metals of an aircraft.

It is another object of the invention to provide detection of hiddencorrosion by way of measuring a phase lag between applied thermal energypulses and temperature cycling of the energized surface.

These and other objects of the invention will become apparent as thedescription of the representative embodiments proceeds.

These and other objects of the invention are achieved by the method ofdetecting. corrosion presence intermediate a workpiece metal substrateand an overlying layer of organic material, said method comprising thesteps of:

-   -   applying a continuing periodic sequence of radiant thermal        energy pulses to said workpiece metal substrate and overlying        layer of organic material:    -   said radiant thermal energy pulses communicating from an        external surface portion of said layer of organic material        through said layer of organic material to said workpiece metal        substrate;    -   sensing instantaneous temperature response undulations of said        surface portion of said workpiece overlying layer of organic        material in response to said continuing periodic sequence of        radiant thermal energy pulses;    -   determining a phase angle of lag between said applied continuing        periodic sequence of radiant thermal energy pulses and said        instantaneous temperature response undulations of said surface        portion of said workpiece overlying layer of organic material;        and    -   examining a workpiece map of said determined phase angles of lag        for a corrosion presence-related pattern of instantaneous        temperature response undulation phase angle variations.

BRIEF DESCRIPTION OF THE DRAWING

The accompanying drawings incorporated in and forming a part of thespecification. illustrate several aspects of the present invention andtogether with the description serve to explain the principles of theinvention. In the drawings:

FIG. 1 shows a military aircraft corrosion detection sequence in whichthe present invention may be used.

FIG. 2 shows details of a corrosion detection sensor usable In the FIG.1 sequence.

FIG. 3 shows additional details of a corrosion detection systemaccording to the present invention.

FIG. 4 shows typical signal waveforms for the FIG. 3 detection system.

FIG. 5 shows a mathematical analysis diagram for the present invention.

FIG. 6 shows a initial time versus temperature relationship for thepresent invention.

FIG. 7 shows an later time versus temperature relationship for thepresent invention.

FIG. 8 shows a terminal time versus temperature relationship for thepresent invention.

FIG. 9 shows a phase lag relationship between paint surface temperatureand heat flux for three different values of thermal conductance in thepresent invention.

FIG. 10 shows a phase difference relationship for two different valuesof thermal conductance for the present invention.

FIG. 11 shows a ripple magnitude relationship for three different valuesof thermal conductance for the present invention.

FIG. 12 shows a ripple magnitude difference for two different values ofthermal conductance for the present invention.

FIG. 13 shows a relationship between phase difference and paintthickness for the present invention.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 in the drawings shows a military aircraft corrosion detectionsequence in which the present invention may be used. In the FIG. 1drawing an operator 104 is shown to be exploring paint hidden portionsof a tactical aircraft 100 in locations believed susceptible to theoccurrence of paint obscured underlying metal corrosion. The region 114of the aircraft 100 adjacent the interface 112 between aircraft radome110 and aircraft fuselage 113 is susceptible to impact “dings” and otherminor physical damage which can admit moisture and airborne corrosiveagents conducive to the formation of paint hidden corrosion of theunderlying aircraft metal. The aluminum, magnesium titanium and otherlightweight high strength metal alloys used In aircraft and spacecraftvehicles are particularly susceptible to such underlying metal orsubsurface corrosion effects. It is of course desirable that any suchcorrosion be detected as soon as possible in order to prevent structuralweakening of the load carrying periphery metal of the aircraft 100 aswell as undesirable unsightly disfigurement of the aircraft. Otherregions of the aircraft 100 believed to be susceptible to paint damaging“dings” or chipping include the interface region 111 between engineinlet cowling and engine housing and the interface region 102 betweencanopy 115 and fuselage 113. Unfortunately, even though airframecorrosion may start with minor damage in the regions 102, 113 and 114 ofan aircraft, it is known to creep in stealth along the interface betweenmetal and paint over extended distances and through relatively complexaircraft contours.

Removal of extensive portions of the paint covering aircraft 100 hasheretofore been practiced not only for the aesthetic purposes describedin the above-identified two patents of T.J. Reinhart, but also for theexclusive purpose of detecting substrate metal corrosion. It is anobject of the present invention to improve on this procedure byproviding a system as represented in the FIG. 1 drawing wherein suchcorrosion can be detected through the paint or other aircraft coating inan early and non-destructive manner. Such detection is provided by wayof the sensing head 106 connected by tether cord 108 to a computerizedcorrosion detection system as is shown in FIG. 3 of the drawings. Thesensing head 106 is shown in the cross sectional view of FIG. 2 in thedrawings to include a source of radiant energy 202, which may beattended by a reflector 204, and by an optical to electrical transducersuch as the video camera 200.

As discussed in some detail below herein, the source of radiant energy202 is preferably operated in an extended cycle of infrared energyemitting pulses according to the present invention. These pulses maymoreover be achieved through use of current modulation of a lamp used toembody the source of radiant energy 202 or through use of mechanicaladditions to the FIG. 2 apparatus, for example, a moving reflectorelement at 204 or a moving optical modulator element as Is representedby the shutter mechanism at 206. The shutter mechanism 206 is especiallyuseful at energy pulsation frequencies above the response capability ofa lamp filament. In lieu of the handheld sensing head 106 shown in FIG.1, the present invention may also be practiced with the use of astationary camera 116 shown to be mounted on a tripod 118 or othersupport and connected by a tether cable 120 to a computerized corrosiondetection system as is shown in FIG. 3. A fixed mounted pulsating heatsource 122 may be used with the fixed camera 116. Notwithstandingadvantages of more stable input data and other possible benefitsavailable with the stationary camera 116 and fixed mounted pulsatingheat source 122, for present discussion purposes use of the handheldsensing head 106 is presumed in the paragraphs following.

FIG. 3 in the drawings shows elements of the sensing head 106 togetherwith a block diagram representation of additional components comprisinga corrosion detection system according to the present invention. In theFIG. 3 drawing there is represented a test sample 309 and a computer 306inclusive array of sensing head control and interface elements 300connecting with a signal processing electronics module 302. Signal flowdirections are indicated as at 304 between the FIG. 3 system components.Generally the FIG. 3 system uses a variable pulse radiant heat source308, a heat source inclusive of the lamp 202 to heat the tested surface310 of the aircraft being inspected for corrosion, and a differentialthermography system including the camera 200 to determine the phase lagbetween a pulsating heater signal and the resulting temperaturevariation of the paint surface at 310.

Differential thermography systems as employed in FIG. 3 are available inthe commercial test instrument marketplace. One system of this type thatmay be used with the present invention has been identified as the StressPhotonics Deltalherm 1000 system that was first made for the U.S. AirForce by Stress Photonics Inc. of 3002 Progress Road, Madison Wisconsin,under the U.S. Government Small Business Innovation Research (SBIR)contract F33615-95-C-2504, which originated at Wright-Patterson AirForce Base. Ohio 45433. Copies of a final report concerning thiscontract and the resulting system, titled “DIFFERENTIAL THERMOGRAPHY FORELEVATED TEMPERATURES” may be obtained from Stress Photonics Inc. andthrough persons including the present inventor at Wright Patterson AirForce Base. The contents of this report are hereby incorporated byreference herein. The F33615-95-C-2504 contract was not/is notclassified.

The DeltaTherm 1000 and similar systems have also been made intocommercial products by Stress Photonics Inc.; such products andtechnical information of the type disclosed in the contract final reportare thus additionally available commercially. Other information relatingto systems of the DeltaTherm 1000 type is understood to have been,published by Dr. Thomas Mackin of The University of Illinois atChampaign-Urbana. Additional differential thermography systems generallyof the DeltaTherm 1000 type are also available commercially, severalnondestructive infrared systems of this nature, including systemsidentified by the names of EchoTherm® and ThermoScope™, are made byThermal Wave Imaging of 845 Livernois Street, Ferndale, Michigan,48220-2308. Their website is http://www.thermalwave.com.

The signal to the “AC Ref Ampl. Input” terminal of the signal processingelectronics 302 in FIG. 3, i.e. the signal on the path 314 in FIG. 3, isrepresentative of the applied radiant flux. This signal may be derivedfrom lamp current pulses by way of, for example, current transformerapparatus 313 in the case of the lower frequency radiant flux, derivedfrom reflector motion signals in the case of moderate frequency radiantflux, and may originate in a heat flux to electrical signal transducerelement 316 located within the heat flux pattern in the case of thehigher frequency shutter controlled radiant flux. A switch, as shown at318 in FIG. 3, may be used to select between these signal inputs inresponse to the needed lamp frequency.

FIG. 4 in the drawings shows the type of signals generated in the FIG. 3system. In FIG. 4 the uppermost signal 402 represents raw camera pixelthermal data as communicated along the path 320 to the “Sig. Input”terminal of the Signal Processing Electronics 302 of the differentialthermography system. The centermost of the FIG. 4 signals, shown at 404represents the temperature variation of the paint surface 310 as it hasbeen extracted from the signal 402 by filtering and amplification. Thissignal 404 may be represented mathematically in terms of a constant, C,and the change of temperature, ΔT, as is shown at 408 in the FIG. 4drawing. Mathematical representation of signal is found to be aconvenience in working with the present invention in that computersimulations and mathematical modeling, as discussed for example inconnection with FIG. 6 through FIG. 8 below herein, may be accomplishedmore rapidly than in the absence of such representation. The lowermostof the FIG. 4 signals, the signal 406 represents pulsations of thethermal flux generated by one of the heater lamps 122 and 206, the typeof signal communicated along the path 314 in the FIG. 3 system. Thepulsations in the signal 406 thus are the source of the other twosignals 404 and 406 in the FIG. 4 drawing and represent the heat fluxstimulation applied to the paint surface 310 in the present invention.

By filtering the thermal signal 402. In FIG. 4, the discloseddifferential thermography systems can detect paint surface 310temperature ripple magnitudes on the order of a few thousandths of adegree Kelvin, i.e. of a few mK. Temperature scales of this magnitudeare shown in the FIG. 6 through FIG. 8 drawings herein. The nature ofthe filtering used in the Stress Photonics DeltaTherm 1000 system toextract the FIG. 4 temperature undulation data 404 from the raw data 402is described in terms of a least squares method and single low frequencyoperation-vector lock-in technique, both of which are disclosedmathematically and in text in appendix B of the above identified finalreport for U.S. Government contract F33615-95-C-2504, titled“DIFFERENTIAL THERMOGRAPHY FOR ELEVATED TEMPERATURES”. Section 3.4 ofthis same report, titled “Variable Amplitude Signal Processing” alsocontains mathematical and text descriptions relevant to the signalprocessing accomplished in the DeltaTherm 1000 differential thermographysystem.

Output signals from the signal processing electonics 302 of thedifferential thermography system appear at the right hand edge of theblock 302 in the FIG. 3 drawing. The uppermost of these signals is thephase output signal and the lowermost is the differential temperatureoutput signal. Both of these signals are communicated to the computer306 along the path 322 for viewing in the manner of the FIG. 4 drawing,for data storage, for control of the camera 200 along path 324 (e.g. forfocal length control) and for possible use by other apparatus employablewith the system.

The phase lag of interest in the present invention, the phase differencebetween the waveforms 406 and 404 in FIG. 4, is indicated at 410 in theFIG. 4 drawing. As has been described earlier herein, this phase lag isfound to be a better and more reliable indicator of corrosion and othereffects Intermediate the metal skin and the paint layer of an aircraftthan are the amplitude measurements used in other corrosion detectionsystems. In observing the FIG. 4 waveforms it may become apparent thatthe instant of heat flux first application, the instant of zero time, isnot shown in the FIG. 4 drawing but occurs somewhere to the left of theleftmost vertical line of the FIG. 4 drawing. The waveforms of FIG. 4therefore represent steady state thermal conditions achieved after apreceding transient period not appearing In FIG. 4. It may also berecognized that each of the waveforms 402, 404 and 406 shown in the FIG.4 drawing are scaled to a different degree with respect to verticalamplitude, i.e., the amplitudes appearing along the left axis of adrawing such as the FIG. 4 drawing.

If a corrosion layer exists in the FIG. 3 test specimen 312, thuscreating a thermal resistance between the paint and the aircraft metal,i.e. the paint substrate, the detected phase lag will change. This phaselag is also a function of the geometric and thermal parameters of thecoated substrate as well as the frequency of the applied heater signal.With respect to corrosion, there are two possibilities that may occur.In the first, the test specimen region examined by the system will beonly partially corroded. In this case a map of the phase lag over thetest specimen region will show the phase difference between the corrodedand undamaged regions. In the second case the entire region beingexamined may be corroded. In this case a map of the phase lag will showa uniform value. In this instance the test specimen map needs to becompared with the phase lag for a non-corroded surface to determine ifcorrosion is present.

The difference in phase lag for values of thermal conductance, h, of 100and 1000 watts per meter²-degree Kelvin CW/m²K) in the FIG. 3 sample 309are shown by the curve 1002 in FIG. 10 of the drawings herein. Similarlythe difference in phase lag for values of thermal conductance, h, of 100and 5000 watts per meter²-degree Kelvin (W/m²K) are shown by the curve1004 In FIG. 10 of the drawings. These FIG. 10 showings of differencebetween two dissimilar values of the variable h are in accordance withthe “Phase Difference Φ(h)-Φ(100)” title for the FIG. 10 drawing. Thevalue of 100 W/m²K corresponds to the presence of a corrosion layer onthe substrate 312 in FIG. 3 and the values of 1000 W/m²K and 5000 W/m²Kcorrespond to two possible cases with no substrate corrosion present Thesubstrate used for the FIG. 10 data is a 2 mm-thick aluminum plate.

As can be seen in FIG. 10, the phase difference between surfacetemperature and thermal energy pulses becomes negligible if thefrequency of the sample heating pulses is too high. A significant aspectof the invention is that the heater frequency can be adjusted to givethe best resolution of corroded areas, depending on the coatingthickness as is shown in FIG. 13 of the drawings herein, where fivedifferent lamp pulsation frequencies appear at 1300 and resultingrelations between paint layer thickness and phase difference appear inthe five curves 1302. In general, thicker coatings require lowerfrequency heat source operation to enable corrosion detection. Byobserving the phase lag at different excitation (heater) frequencies,optimum discrimination between signals caused by corrosion and othernon-uniformities in the sample system can be obtained.

The optimum operating frequency of the radiant heating system of thepresent invention, i.e., the heater pulse rate, can be expected to liebetween 0.1 and 30 Hz. The methods of controlling the frequency of theincident energy depend on the frequencies needed and range from a simplecontrol of the power to the heater or lamp 202 for low frequencyoperation to an oscillating reflector(s) 204 for slightly higherfrequencies to a shutter system 206 for still higher frequencies. Theshutter system 206 may, for example, periodically admit energy from thelamp 202 to the painted surface 310 and obscure the painted surfacei.e., capture energy in a heat-sinking element. The switch 318 In theFIG. 3 system may be used to select the appropriate input signal for thedifferential thermography system according to which of these heat fluxmodulating arrangements is employed for a particular test.

The three curves of FIG. 9 in the drawings show the phase lag betweenthe surface temperature and the Incident heat flux for a paint thicknessof 0.254 millimeter and for the three different values of thermalconductance, h₁, described above with respect to the FIG. 10 drawing.The FIG. 9 conductance values therefore represent three differingcorrosion conditions. The phase lag shown in these plots is dependent onthe thermal conductance, h₁, and the heater frequency. These curves alsoillustrate that the heater frequency should be selected to beappropriate for the paint thickness used. If the heater pulse frequencyis too high the phase lag is the same regardless of the hi conductancevalue and the related test is thus not a desirable indicator ofcorrosion presence.

The three curves of FIG. 11 in the drawings show the magnitude of thesinusoidal ripple superimposed on the average surface temperature of thesurface 310 in the FIG. 3 test system. The differential thermographyapparatus of the FIG. 3 system filters the total signal obtained fromthe surface 310 and separates the ripple component of the signal as isdescribed above herein. It may be noted in the FIG. 11 relationshipsthat the ripple magnitude observed is small for the low level incidentenergy (i.e., q_(o)=10 W/m²) used for the FIG. 11 simulation (thevertical scale in the FIG. 11 drawing represents observed rippleamplitude multiplied by a factor of 1000). Low level incident energy isdesirable in-present invention testing because the surface temperaturewill change by only a few degrees but this condition also makes itharder to detect the ripple magnitude achieved therefore some compromiseis appropriate. The relatively small magnitude of the ripple to beobserved in the present invention and the importance of radiant fluxfrequency selection in order to obtain desirable ripple amplitude mayalso be appreciated from the FIG. 11 relationships. FIG. 12 shows thedata from two of the FIG. 11 curves in alternate form and emphasizes therelatively small ripple observations made in connection with the FIG. 11data.

FIG. 6 in the drawings shows the manner in which the surface 301 in FIG.3 or the surface of the test aircraft 100 in FIG. 1 can be expected tochange in response to the pulsations of thermal energy provided in theFIG. 3 system during the first several seconds after energy application.The two different curves in the FIG. 6 data represent two differentapproaches to simulating the temperature changes occurring during a FIG.3 test. The data of the solid line curve 600 in FIG. 6 represents anumerical approximation of the relationships defined in an analyticalsolution for temperature T₁ according to equation 1 in the followingmathematical discussion of the present invention. The data of the dottedline curve 602 in FIG. 6 represents an analytical solution fortemperature T₂ in equation 12 in the following mathematical discussionof the present invention.

A notable aspect of the FIG. 6 data from these two sources lies in thesimilar results obtained from the two differing temperature predictionapproaches. Such similarity enhances confidence with respect to theaccuracy of the differential temperature results predicted. The curvesin FIG. 7 in the drawings show the FIG. 6 data over a longer period oftime. FIG. 8 of the drawings shows a yet longer-term representation ofthe surface temperatures occurring during a measurement according to thepresent invention. The FIG. 8 data (which is actually also two curves inclosed superposition) may be regarded as the terminal time versustemperature relationship for a test according to the present invention;these curves display the asymptotic nature of the temperature in theright-hand portion of the FIG. 8 curve. The relatively small incrementsof temperature shown along the vertical axes of the FIG. 6 through FIG.8 drawings are in keeping with the relatively small thermal fluxmagnitudes discussion above.

FIG. 5 in the drawings shows a test sample 500 of an aircraft skinsurface 502 covered by a layer of paint 504 and undergoing incidentradiation infrared heat gain, as is indicated at 506. The FIG. 5 testsample 500 is also experiencing convection heat loss to the ambient asindicated at 508. The skin metal at 502 is also identified as region 1in the FIG. 5 drawing and is assumed to have the thickness L₁ indicatedat 510 in the drawing. The overall skin surface 502 in has the thicknessL indicated at 512 in FIG. 5. The paint coating 504 on the skin surfacemetal 502 is also identified as region 2 in the FIG. 5 drawing and has athickness of L-L₁. The FIG. 5 sample 500 may be considered to provide adefinitional basis for the following mathematical consideration of thepresent invention.

For the following mathematical consideration, FIG. 5 may be regarded asshowing an aluminum plate with corrosion at the interface between thealuminum and the paint. The effect of the corrosion layer is modeled bya change in the thermal conductance, h₁, between the paint and thesubstrate. If there is no corrosion and the thermal contact is perfect,the conductance h₁ is infinite. This corresponds to zero resistance toheat conduction. In real systems the conductance has a large value butis not infinite. As the surface begins to corrode, the thermalconductance decreases and the corrosion layer acts like a thermalinsulator. This means less energy will be conducted into the substrateand more will be lost to the environment. It is expected that the changein conductance is similar to that due to surface roughness; aconductance which decreases from 1050 W/m²C to 250 W/m²C for 75S-T6Aluminum as the roughness increases from 0.254 millimeter to 0.3millimeter. A mathematical model of the system shown in FIG. 5 solvesthe heat conduction equation in each layer with additional boundaryconditions between layers to account for the thermal conductance at theinterface. The heat conduction equation for each region and theassociated boundary conditions are given as equations 1.a-d and 2.a-b.Equations 1.b-c, specify that the heat flux is continuous across theinterface but the temperature is discontinuous, with the differencebeing controlled by the value of h₁. It is assumed that the system andthe surroundings are initially at a uniform temperature T_(o). At t=0,the painted surface at x=L, is heated by incident radiation such thatthe absorbed part of the radiant energy is given by q0(1+Asin(ωt)). Theback surface at x=0 is considered to be insulated but the results shouldnot be significantly different if heat transfer by convection orradiation is included. $\begin{matrix}{{Region}\quad 1.} & \quad \\\begin{matrix}{{\alpha_{1}\frac{\partial^{2}T_{1}}{\partial x^{2}}} = \frac{\partial T_{1}}{\partial t}} & {0 < x < L_{1;}} & {t > 0}\end{matrix} & (1.) \\\begin{matrix}{\frac{\partial T_{1}}{\partial x} = 0} & {{x = 0};} & {t > 0}\end{matrix} & \left( {1.a} \right) \\\begin{matrix}{{{- k_{1}}\frac{\partial T_{1}}{\partial x}} = {h_{1}\left( {T_{1} - T_{2}} \right)}} & {{x = L_{1}};} & {t > 0}\end{matrix} & \left( {1.b} \right) \\\begin{matrix}{{k_{1}\frac{\partial T_{1}}{\partial x}} = {k_{2}\frac{\partial T_{2}}{\partial x}}} & {{x = L_{1}};} & {t > 0}\end{matrix} & \left( {1.c} \right) \\\begin{matrix}{T = T_{o}} & {{0 < x < L_{1}};} & {t = 0}\end{matrix} & \left( {1.d} \right) \\{{Region}\quad 2.} & \quad \\{{{\alpha_{2}\frac{\partial T_{2}}{\partial x^{2}}} = {{\frac{\partial T_{2}}{\partial x}\quad L_{1}} < x < L}};\quad{t > 0}} & (2.) \\{{{{k_{2}\frac{\partial T_{2}}{\partial x}} + {h_{2}T_{2}}} = {{{h_{2}\left\lbrack \underset{f{(t)}}{\underset{︸}{T_{\infty} + \frac{q_{o}\left( {1 + {A\quad{\sin\left( {\omega\quad t} \right)}}} \right)}{h_{2}T_{o}}}} \right\rbrack}\quad x} = L}};\quad{t > 0}} & \left( {2.a} \right) \\{{T_{2} = {{T_{o}\quad x} < L_{1} < L}};\quad{t = 0}} & \left( {2.b} \right)\end{matrix}$This problem can be solved using a Green's function approach forcomposite media as given by Ozisik.[1] The problem is first transformedusing:T _(i)(x,t)=θ_(i)(x,t)+ξ_(i)(x)f(t)   (3)to remove the non-homogeneous boundary condition at x=L which results ina time dependent volumetric heat source term in the heat conditionequation. The subscript, i=1,2 refers to the regions 1 and 2. f(t) isdefined in eq. (2.a); θ and ν are the solutions to the followingauxiliary problems. $\begin{matrix}{{Region}\quad 1.} & \quad \\{{{{\alpha_{1}\frac{\partial^{2}\theta_{1}}{\partial x^{2}}} - {\xi_{1}\frac{\mathbb{d}{f(t)}}{\mathbb{d}t}}} = {{\frac{\partial\theta_{1}}{\partial t}\quad 0} < x < L_{1}}};\quad{t > 0}} & (4.) \\{{\frac{\partial\theta_{1}}{\partial x} = {{0\quad x} = 0}};\quad{t > 0}} & \left( {4.a} \right) \\{{{{- k_{1}}\frac{\partial\theta_{1}}{\partial x}} = {{{h_{1}\left( {\theta_{1} - \theta_{2}} \right)}\quad x} = L_{1}}};\quad{t > 0}} & \left( {4.b} \right) \\{{{k_{1}\frac{\partial\theta_{1}}{\partial x}} = {{k_{2}\frac{\partial\theta_{2}}{\partial x}\quad x} = L_{1}}};\quad{t > 0}} & \left( {4.c} \right) \\{{{\theta_{1}(0)} = {{T_{o} - {{f(0)}\quad 0}} < x < L_{1}}};\quad{t = 0}} & \left( {4.d} \right) \\{{Region}\quad 2.} & \quad \\{{{{\alpha_{2}\frac{\partial\theta_{2}}{\partial x^{2}}} - {\xi_{2}\frac{\mathbb{d}{f(t)}}{\mathbb{d}t}}} = {{\frac{\partial\theta_{2}}{\partial x}\quad L_{1}} < x < L}};\quad{t > 0}} & (5.) \\{{{{k_{2}\frac{\partial\theta_{2}}{\partial x}} + {h_{2}\theta_{2}}} = {{0\quad x} = L}};\quad{t > 0}} & \left( {5.a} \right) \\{{\theta_{2}(0)} = {{{T_{o} - {{f(0)}\quad L_{1}}} < x < {L\quad t}} = 0}} & \left( {5.b} \right) \\{{Region}\quad 1.} & \quad \\{\frac{\partial^{2}\xi_{1}}{\partial x^{2}} = {{0\quad 0} < x < L_{1}}} & (6) \\{\frac{\partial\xi_{1}}{\partial x} = {{0\quad x} = 0}} & \left( {6.a} \right) \\{{{- k_{1}}\frac{\partial\xi_{1}}{\partial x}} = {{{h_{1}\left( {\xi_{1} - \xi_{2}} \right)}\quad x} = L_{1}}} & \left( {6.b} \right) \\{{k_{1}\frac{\partial\xi_{1}}{\partial x}} = {{k_{2}\frac{\partial\xi_{2}}{\partial x}\quad x} = L_{1}}} & \left( {6.c} \right) \\{{Region}\quad 2.} & \quad \\{\frac{\partial^{2}\xi_{2}}{\partial x^{2}} = {{0\quad L_{1}} < x < L}} & (7) \\{{{k_{2}\frac{\partial\xi_{2}}{\partial x}} + {h_{2}\xi_{2}}} = {{h_{2}\quad x} = L_{1}}} & \left( {7.a} \right)\end{matrix}$For this problem, ξ₁=ξ₂ and reduce to 1.The solution for θ_(i)(x,t) can be written in terms of Green's functionas: $\begin{matrix}{{\theta_{i}\left( {x,t} \right)} = {\sum\limits_{j = 1}^{2}\left\{ {\int_{x_{j}}^{x_{j + 1}}{{G_{ij}\left( {x,\left. t \middle| x^{\prime} \right.,\tau} \right)}\left. _{\tau = 0}{{{F_{j}\left( x^{\prime} \right)}{\mathbb{d}x^{\prime}}} + {\int_{\tau = 0}^{t}{\int_{x_{j}}^{x_{j + 1}}{{{G_{ij}\left( {x,\left. t \middle| x^{\prime} \right.,\tau} \right)}\left\lbrack {\frac{\alpha_{j}}{k_{j}}{g_{j}\left( {x^{\prime},\tau} \right)}} \right\rbrack}{\mathbb{d}x^{\prime}}{\mathbb{d}\tau}}}}} \right\}}} \right.}} & (8)\end{matrix}$Where the Green's function is defined as: $\begin{matrix}{{G_{ij}\left( {x,\left. t \middle| x^{\prime} \right.,\tau} \right)} = {\sum\limits_{n = 1}^{\infty}\frac{{{\mathbb{e}}^{- {\beta_{n}^{2}{({t - \tau})}}}\left( \frac{k_{j}}{\alpha_{j}} \right)}{\Psi_{i\quad n}(x)}{\Psi_{jn}\left( x^{\prime} \right)}}{N_{n}}}} & (9)\end{matrix}$The normalization integral is: $\begin{matrix}{N_{n} = {\sum\limits_{j = 1}^{2}{\left( \frac{k_{j}}{\alpha_{j}} \right){\int_{x_{j}}^{x_{j + 1}}{{\Psi_{jn}^{2}(x)}\quad{\mathbb{d}x}}}}}} & (10)\end{matrix}$The eigenfunctions are: $\begin{matrix}{{\Psi_{i\quad n}\left( x^{*} \right)} = {{A_{i\quad n}{\sin\left( \frac{\beta_{n}{Lx}^{*}}{\sqrt{\alpha_{i}}} \right)}} + {B_{i\quad n}{\cos\left( \frac{\beta_{n}{Lx}^{*}}{\sqrt{\alpha_{i}}} \right)}}}} & (11)\end{matrix}$The eigenvalues β_(n) and constants A_(in) and B_(in) are determinedfrom the boundary conditions to arrive at a solution for θ_(i)(x,t)which is then substituted into equation 3 for T_(i)(x,t). For thisproblem, only the surface temperature is desired. This can be writtenas: $\begin{matrix}{{T_{2}\left( {L,t} \right)} = {T_{\infty} + {\frac{q_{o}}{h_{2}}\left\{ {1 + {A\quad{\sin\left( {\omega\quad t} \right)}} - {\sum\limits_{n = 1}^{\infty}\left\lbrack {{C_{i\quad n}{\mathbb{e}}^{{- \beta_{n}^{2}}t}} + {A\quad\omega\quad C_{n}{\sin\left( {{\omega\quad t} + \phi_{n}} \right)}}} \right\rbrack}} \right\}}}} & (12)\end{matrix}$where $\phi_{n} = \frac{\beta^{2}n}{\omega}$ $\begin{matrix}{C_{i\quad n} = {{\frac{\Psi_{2n}(L)}{N_{n}}\left\lbrack {1 - \frac{A\quad\omega\quad\beta_{n}^{2}}{\beta_{n}^{4} + \omega^{2}}} \right\rbrack}\left\{ {{\frac{k_{1}}{\alpha_{1}}{\int_{0}^{L_{1}}{{\Psi_{1n}(x)}\quad{\mathbb{d}x}}}} + {\frac{k_{2}}{\alpha_{2}}{\int_{L_{1}}^{L}{{\Psi_{2n}(x)}\quad{\mathbb{d}x}}}}} \right\}}} & (13) \\{C_{n} = {\frac{\Psi_{2n}(L)}{N_{n}\sqrt{\beta_{n}^{2} + \omega^{2}}}\left\{ {{\frac{k_{1}}{\alpha_{1}}{\int_{0}^{L_{1}}{{\Psi_{1n}(x)}\quad{\mathbb{d}x}}}} + {\frac{k_{2}}{\alpha_{2}}{\int_{L_{1}}^{L}{{\Psi_{2n}(x)}\quad{\mathbb{d}x}}}}} \right\}}} & (14)\end{matrix}$The eigenvalues are found by setting the determinent given in equation15 equal to zero. $\begin{matrix}{\begin{matrix}{{\frac{\gamma_{1}}{H_{1}}{\sin\left( {\gamma_{1}L_{1}} \right)}} - {\cos\left( {\gamma_{1}L_{1}} \right)}} & {\sin\left( {\gamma_{2}L_{1}} \right)} & {\cos\left( {\gamma_{2}L_{1}} \right)} \\{\frac{k_{1}}{k_{2}}\sqrt{\frac{\alpha_{2}}{\alpha_{1}}}{\sin\left( {\gamma_{1}L_{1}} \right)}} & {\cos\left( {\gamma_{2}L_{1}} \right)} & {- {\sin\left( {\gamma_{2}L_{1}} \right)}} \\0 & {{\gamma_{2}{\cos\left( {\gamma_{2}L} \right)}} + {H_{2}{\sin\left( {\gamma_{2}L} \right)}}} & {{{- \gamma_{2}}{\sin\left( {\gamma_{2}L} \right)}} + {H_{2}{\cos\left( {\gamma_{2}L} \right)}}}\end{matrix}} & (15)\end{matrix}$where${H_{i} = {h_{i}/k_{i}}};{\gamma_{i} = \frac{\beta_{n}}{\sqrt{\alpha_{i}}}}$The exponential term in equation (12) can be filtered out and the otherterms combined to give:T_(f)(L,t)=(ωt+φ)   (16)where $\begin{matrix}{C = \sqrt{\left\lbrack {\sum\limits_{n = 0}^{\infty}{C_{n}{\cos\left( \phi_{n} \right)}}} \right\rbrack^{2} + \left\lbrack {\sum\limits_{n = 0}^{\infty}{C_{n}{\sin\left( \phi_{n} \right)}}} \right\rbrack^{2}}} & (17) \\{\phi = {{\tan^{- 1}\left( \frac{\sum\limits_{n = 0}^{\infty}{C_{n}{\sin\left( \phi_{n} \right)}}}{\sum\limits_{n = 0}^{\infty}{C_{n}{\cos\left( \phi_{n} \right)}}} \right)} - \pi}} & (18)\end{matrix}$

The phase angle φ is seen to be a function of the parameters, L₁, L, k₁,k₂, α₁, α₂, h₁, h₂, qo and ω. The dependence on h₁ makes φ useful forcorrosion detection because the thermal conductance changes whencorrosion is present.

Reflected energy from the lamp to the detector will be at the loadfrequency but with a negligible phase lag.

-   If the coating is radiatively gray:    q^(″) _(r)=(1−ε)F₁₆₋₂₄₀₀₀(λT)F_(s-d)q_(o)(1+Asin(ωt))    This can be subtracted from the detector signal. For a 2000° K.    source F₁₆₋₂₄₀₀₀(λT)≈0.0171, i.e., 98% of the radiation is outside a    detector range of 8-12μm.    The view factor will cause a change in magnitude of detected    temperature signal but should not affect the phase lag.

The sensitivity of φ to the different parameters may be examined, i.e.,$\begin{matrix}{S_{i} = \frac{\partial\phi}{\partial z_{i}}} & (19)\end{matrix}$This relationship may be used to seek a method of data analysis that isInsensitive to paint thickness. reflectance, and view factor but issensitive to conductance between paint and aluminum.

The present invention therefore appears to offer several advantages withrespect to other arrangements for inspecting aircraft and otherstructures for the presence of hidden corrosion. Among these advantagesare the characteristics of the disclosed system being:

-   -   Non-contacting    -   Sensitive to the corrosion layer    -   Insensitive to coating thickness, emissivity    -   Insensitive to substrate dimensions    -   Insensitive to sensor view factor (i.e., perpendicularity of the        camera with respect to the aircraft surface)    -   Quick    -   Inexpensive    -   Able to be used to detect patches of corrosion or existence of        corrosion if It is located over the entire region of interest

The foregoing description of the preferred embodiment has been presentedfor purposes of illustration and description. It is not intended to beexhaustive or to limit the invention to the precise form disclosed.Obvious modifications or variations are possible in light of the aboveteachings. The embodiment was chosen and described to provide the bestillustration of the principles of the invention and its practicalapplication to thereby enable one of ordinary skill in the art toutilize the invention in various embodiments and with variousmodifications as are suited to the particular scope of the invention asdetermined by the appended claims when interpreted in accordance withthe breadth to which they are fairly, legally and equitably entitled.

1. A method of detecting corrosion presence intermediate an aircraftworkpiece metal substrate and an overlying layer of organic material,said method comprising the steps of: applying a continuing periodicsequence of radiant thermal energy pulses of repetition frequency belowten Hertz to said aircraft workpiece metal substrate and overlying layerof organic material; said radiant thermal energy pulses communicatingfrom an external surface portion of said layer of organic materialthrough said layer of organic material to said aircraft workpiece metalsubstrate; sensing instantaneous temperature response undulations ofsaid surface portion of said aircraft workpiece overlying layer oforganic material in response to said continuing periodic sequence ofradiant thermal energy pulses; determining a phase angle of lag betweensaid applied continuing periodic sequence of radiant thermal energypulses and said instantaneous temperature response undulations of saidsurface portion of said workpiece overlying layer of organic material;and examining a workpiece map of said determined phase angles of lag fora corrosion presence-related pattern of instantaneous temperatureresponse undulation phase angle variations.
 2. The method of detectingcorrosion presence intermediate an aircraft workpiece metal substrateand an overlying layer of organic material of claim 1 further includingthe step of optimizing said instantaneous temperature responseundulations of said surface portion of said workpiece overlying layer oforganic material by altering at least one of a pulse durationcharacteristic and a pulse frequency characteristic of said continuingperiodic sequence of radiant thermal energy pulses.
 3. The method ofdetecting corrosion presence intermediate an aircraft workpiece metalsubstrate and an overlying layer of organic material of claim 1 whereinsaid step of sensing instantaneous temperature response undulations ofsaid surface portion of said aircraft workpiece overlying layer oforganic material includes the step of enhancing a relative amplitude ofa signal relating to said instantaneous temperature response undulationsof said surface portion of said workpiece-overlying layer of organicmaterial with respect to: extraneous noise signals components byfiltering said signal relating to said instantaneous; temperatureresponse undulations of said surface portion of said workpiece.
 4. Themethod of detecting corrosion presence intermediate an aircraftworkpiece metal substrate and an overlying layer of organic material ofclaim 1 wherein said aircraft workpiece metal substrate comprises ametal skin portion of said aircraft and said overlying layer of organicmaterial comprises an organic material coating on said aircraft metalskin portion.
 5. The method of detecting corrosion presence intermediatean aircraft workpiece metal substrate and an overlying layer of organicmaterial of claim 4 wherein said aircraft workpiece metal substratecomprises an aluminum inclusive metal skin portion of an aircraft. 6.The method of detecting corrosion presence intermediate an aircraftworkpiece metal substrate and an overlying layer of organic material ofclaim 4 wherein said step of applying a continuing periodic sequence ofradiant thermal energy pulses of frequency below ten Hertz to saidaircraft workpiece metal substrate and overlying layer of organicmaterial includes a step of generating said continuing periodic sequenceof radiant thermal energy pulses through one of: modulating electricalcurrent flowing to an electrical energy to thermal energy transducerelement generating said radiant thermal energy to generate said pulsesof radiant thermal energy, shutter modulating an optical output of anelectrical energy to thermal energy transducer element generating saidradiant thermal energy to generate said pulses of radiant thermalenergy, and altering a mechanical position of an optical reflectorelement associated with an electrical energy to thermal energytransducer element generating said radiant thermal energy to generatesaid pulses of radiant thermal energy.
 7. The method of detectingcorrosion presence intermediate an aircraft workpiece metal substrateand an overlying layer of organic material of claim 1 further includingthe step of controlling said step of applying a continuing periodicsequence of radiant thermal energy pulses of frequency below ten Hertzto said aircraft workpiece metal substrate and overlying layer oforganic material in order to optimize a relationship between aircraftworkpiece temperature rise and amplitude of said instantaneoustemperature response undulations.
 8. An apparatus responsive tocorrosion presence intermediate an aircraft component workpiece metalsubstrate and an overlying layer of organic material, said apparatuscomprising the combination of: means for applying a continuing periodicsequence of radiant thermal energy pulses of frequency below ten Hertzto said workpiece metal substrate and said overlying layer of organicmaterial; said radiant thermal energy pulses communicating from anexternal surface portion of said layer of organic material through saidlayer of organic material to said aircraft component workpiece metalsubstrate; means for sensing instantaneous temperature responseundulations of said surface portion of said aircraft component workpieceoverlying layer of organic material in response to said continuingperiodic sequence of radiant thermal energy pulses; means fordetermining a phase angle of lag between said applied continuingperiodic sequence of radiant thermal energy pulses and saidinstantaneous temperature response undulations of said surface portionof said aircraft component workpiece overlying layer of organicmaterial; and means for generating an aircraft component workpiece mapof said determined phase angles of lag, said map including a corrosionpresence-related pattern of instantaneous temperature responseundulation phase angle variations.
 9. The apparatus responsive tocorrosion presence intermediate a an aircraft workpiece metal substrateand an overlying layer of organic material of claim 8 wherein said meansfor applying a continuing periodic sequence of radiant thermal energypulses to said aircraft workpiece includes one of a controllable lampcurrent modulator apparatus, a movable lamp reflector and an opticalenergy modulator apparatus.
 10. The apparatus responsive to corrosionpresence intermediate an aircraft workpiece metal substrate and anoverlying layer of organic material of claim 8 wherein said means forapplying a continuing periodic sequence of radiant thermal energy pulsesto said workpiece metal substrate and said overlying layer of organicmaterial further includes control means for modifying a timecharacteristic of said continuing periodic sequence of radiant thermalenergy pulses and increasing said sensed instantaneous temperatureresponse undulations of said surface portion of said workpiece overlyinglayer of organic material.
 11. A contact free method of detectingcorrosion presence intermediate a covered metal skin portion of anaircraft and an overlying paint coating layer, said method comprisingthe steps of: applying a continuing periodic sequence of infraredradiant thermal energy pulses of selected pulse frequency below tenHertz to an external surface region of said overlying paint coatinglayer of said aircraft; said radiant thermal energy pulses communicatingthermal energy from said external surface region of said overlying paintcoating layer through said paint coating layer and into said coveredmetal skin portion of said aircraft at a first rate in aircraft metalskin regions free of corrosion presence and at a lesser second rate inaircraft metal skin regions having corrosion presence intermediate saidoverlying paint coating layer and said metal skin portion; opticallysensing overlying paint coating layer external surface regioninstantaneous temperature response undulations responding to saidcontinuing periodic sequence of radiant thermal energy pulses;determining a phase angle of lag between said applied continuingperiodic sequence of radiant thermal energy pulses and said overlyingpaint coating layer external surface region instantaneous temperatureresponse undulations; examining an aircraft metal skin portion surfacemapping of said determined phase angles of lag for a corrosionpresence-related disturbed pattern of instantaneous temperature responseundulation phase angles; and selecting time and frequencycharacteristics of said continuing periodic sequence of infrared radiantthermal energy pulses in response to achieving one of an increasedamplitude of said optically sensed overlying paint coating layerexternal surface region instantaneous temperature response undulationsand an increased phase angle of lag between said applied continuingperiodic sequence of radiant thermal energy pulses and said overlyingpaint coating layer external surface region instantaneous temperatureresponse undulations.